Sciweavers

45
Voted
MICS
2010

Arrangements on Parametric Surfaces II: Concretizations and Applications

13 years 6 months ago
Arrangements on Parametric Surfaces II: Concretizations and Applications
We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arrangements embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The fundamentals of the framework are described in a companion paper. Our work covers arrangements embedded on elliptic quadrics and cyclides induced by intersections with other algebraic surfaces, and a specialized case of arrangements induced by arcs of great circles embedded on the sphere. We also demonstrate how such arrangements can be used to accomplish various geometric tasks efficiently, such as computing the Minkowski sums of polytopes, the envelope of surfaces, and Voronoi diagrams embedded on parametric surfaces. We do not assume general position. Namely, we handle degenerate input, and produce exact results in all cases. Our implementation is realized using Cgal and, in particular, the package th...
Eric Berberich, Efi Fogel, Dan Halperin, Michael K
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where MICS
Authors Eric Berberich, Efi Fogel, Dan Halperin, Michael Kerber, Ophir Setter
Comments (0)